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Abstract

Light shifts are an important source of noise and systematics in optically pumped magnetometers. We demonstrate that the long spin-coherence time in paraffin-coated cells leads to spatial averaging of the vector light shift over the entire cell volume. This renders the averaged vector light shift independent, under certain approximations, of the light-intensity distribution within the sensor cell. Importantly, the demonstrated averaging mechanism can be extended to other spatially varying phenomena in anti-relaxation-coated cells with long coherence times.

Figures (4)

a) The experimental setup. The amplitude-modulated, circularly polarized pump beam propagates along ẑ (orthogonally to B⃗0 ‖ ŷ). A local oscillator (LO) pulses the pump intensity via an acousto-optical modulator (AOM) and serves as a reference for a lock-in amplifier (LIA), whose analog output is recorded with a data acquisition card (DAQ) and stored on a computer (PC). After transmitting through the cell, the linearly polarized probe beam is analyzed with a balanced polarimeter, consisting of a polarizing beam splitter (PBS) and two photodiodes. The circularly polarized light-shift beam (LS beam) propagates along B⃗0. Its diameter is varied with a computer controlled, motorized iris while its time-averaged power is kept constant with an AOM in a feedback loop. An image of the iris is formed inside the cell and on the beam profiler using a lens system. The optical frequency of the LS beam is measured with a wavemeter and controlled by the PC. For noise reduction, we perform synchronous detection of the VLS signal while harmonically modulating the LS beam power at ωM. b) shows the recorded time series for the LIA Y output for a single light shift measurement with the simultaneous modulation of the LO frequency and the LS power. c) The FFT of the signal in b) shows the calibration peak at ωC/2π and the LS amplitude at ωM/2π.

Change of the magnetic resonance center frequency as a function of the light-shift beam area for different LS beam detunings and a constant beam power. The complete data include detunings from −60 GHz to +60 GHz with respect to the 133Cs D1F = 4 transitions. Just a fraction of the data is displayed here for better visibility of the individual sets. While the beam area x, and therefore the beam intensity, is modified by an order of magnitude, the MR center frequency changes are on average 3% and are of technical origin as explained in the text. Different colors represent distinct optical frequencies of the LS beam, the detuning is indicated by the arrows on the right. The data points are represented by circles, and the lines are linear fits δνLS (x) = aLS + bLS (x − 〈x〉) to the datasets. 〈x〉 is the mean area of the fitted set. The fit parameters are average light shift aLS and light shift change per unit area change bLS.

Average vector light shift aLS dependence on the optical frequency as derived from the fits to the data displayed in Fig. 2. The error bars are hidden within the points since the average ratio between data value and error is 140. The red curve shows a fit to the data with ∝ 1/ΔLS.

Light-shift change per unit area bLS divided by the average light-shift aLS (bLS/aLS from Fig. 2) as a function of the LS beam detuning. The data were rescaled to express the change of the measured light shift over each dataset to its mean value in percent. The red line is a sinusoidal fit revealing an etalon effect potentially in the cell wall.